Phenomenological model for the $\gamma \gamma \to {\pi }^{+}{\pi }^{-}{\pi }^0$ reaction

Abstract

We present a phenomenological model for the $\gamma \gamma \to {\pi }^{+}{\pi }^{-}{\pi }^0$ reaction by including the production mechanism of the $a_2(1320)$ resonance, as well as the contributions from the $\sigma /f_0(500){\pi }^0$ and $f_2(1270){\pi }^0$ production channels. Furthermore, the $\gamma \gamma \to {\rho }^{\pm }{\pi }^{\mp }\to {\pi }^{+}{\pi }^{-}{\pi }^0$ channel, which is essential for a description in the low-energy region, is investigated carefully by introducing the complete set of gauge invariant and Lorentz-covariant tensors for the $\gamma \gamma \to {\rho }^{\pm }{\pi }^{\mp }$ subprocess. The full amplitude is constructed to yield a correct high-energy Regge behavior. Within our model, we achieve a very reasonable description of ARGUS and L3 data of the total cross section, as well as of the ${\pi }^{\pm }{\pi }^0$ and ${\pi }^{+}{\pi }^{-}$ invariant mass distributions. We also predict the invariant mass distributions in the $\gamma \gamma$ center-of-mass energy range from $0.8$ GeV to $2.0$ GeV, which will be studied by the forthcoming data of the BESIII collaboration.

12 pages, 6 figures, 1 table; matches the published version

References in corpus (5)

• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• MO analysis of the high statistics Belle results on $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ with chiral constraints
• Dispersion relations for ${\gamma }^{\ast }{\gamma }^{\ast }\to \pi \pi$: helicity amplitudes, subtractions, and anomalous thresholds
• The hadronic light-by-light contribution to the muon's anomalous magnetic moment
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations